What is the relationship between gravitational potential and gravitational field

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Question: What is the relationship between gravitational potential and gravitational field strength?

Options:

Correct Answer: g = -dV/dr

Solution:

The gravitational field strength g is the negative gradient of the gravitational potential V, given by g = -dV/dr.

What is the relationship between gravitational potential and gravitational field strength?

What is the relationship between gravitational potential and gravitational field strength?

Correct Answer: g = -dV/dr

Step 1: Understand that gravitational potential (V) is a measure of the potential energy per unit mass at a point in a gravitational field.
Step 2: Recognize that gravitational field strength (g) is the force experienced by a unit mass in that field.
Step 3: Learn that the relationship between gravitational potential and gravitational field strength is based on how potential changes with distance.
Step 4: The term 'gradient' refers to how steeply something changes. In this case, it means how quickly gravitational potential changes as you move away from a mass.
Step 5: The formula g = -dV/dr shows that gravitational field strength (g) is equal to the negative change in gravitational potential (dV) with respect to distance (dr).
Step 6: The negative sign indicates that as you move away from a mass, the gravitational potential decreases, while the gravitational field strength points towards the mass.

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